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Complex dynamics and switching transients in periodically forced Filippov prey–predator system

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  • Tang, Guangyao
  • Qin, Wenjie
  • Tang, Sanyi

Abstract

By employing threshold policy control (TPC) in combination with the definition of integrated pest management (IPM), a Filippov prey–predator model with periodic forcing has been proposed and studied, and the periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. This study aims to address how the periodic forcing and TPC affect the pest control. To do this, the sliding mode dynamics and sliding mode domain have been addressed firstly by using Utkin’s equivalent control method, and then the existence and stability of sliding periodic solution are investigated. Furthermore, the complex dynamics including multiple attractors coexistence, period adding sequences and chaotic solutions with respect to bifurcation parameters of forcing amplitude and economic threshold (ET) have been investigated numerically in more detail. Finally the switching transients associated with pest outbreaks and their biological implications have been discussed. Our results indicate that the sliding periodic solution could be globally stable, and consequently the prey or pest population can be controlled such that its density falls below the economic injury level (EIL). Moreover, the switching transients have both advantages and disadvantages concerning pest control, and the magnitude and frequency of switching transients depend on the initial values of both populations, forcing amplitude and ET.

Suggested Citation

  • Tang, Guangyao & Qin, Wenjie & Tang, Sanyi, 2014. "Complex dynamics and switching transients in periodically forced Filippov prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 13-23.
    • Handle: RePEc:eee:chsofr:v:61:y:2014:i:c:p:13-23
    DOI: 10.1016/j.chaos.2014.02.002
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    References listed on IDEAS

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    1. Tang, Sanyi & Xiao, Yanni & Cheke, Robert A., 2008. "Multiple attractors of host–parasitoid models with integrated pest management strategies: Eradication, persistence and outbreak," Theoretical Population Biology, Elsevier, vol. 73(2), pages 181-197.
    2. Yang, F.H. & Zhang, W. & Wang, J., 2009. "Sliding bifurcations and chaos induced by dry friction in a braking system," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1060-1075.
    3. Singh, Brajendra K. & Gambhir, Manoj & Hu, Chin-Kun, 2008. "Quasi-cycles and sensitive dependence on seed values in edge of chaos behaviour in a class of self-evolving maps," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 641-649.
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    Cited by:

    1. Qin, Wenjie & Tang, Sanyi, 2014. "The selection pressures induced non-smooth infectious disease model and bifurcation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 160-171.
    2. Li, Wenxiu & Chen, Yuming & Huang, Lihong & Wang, Jiafu, 2022. "Global dynamics of a filippov predator-prey model with two thresholds for integrated pest management," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Wenjie Qin & Zhengjun Dong & Lidong Huang, 2024. "Impulsive Effects and Complexity Dynamics in the Anti-Predator Model with IPM Strategies," Mathematics, MDPI, vol. 12(7), pages 1-25, March.

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